Indian Numeral System
The Indian numeral system is a writing system adapted in India for expressing numbers. It is a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner. This numeral system comprises a set of numerals formed by 10 symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
Long before numbers were invented, a unique mark was made on each item being counted. This was a complex system for writing large numbers. It was realized that there was a need to adopt a standard system of counting. This is how the numeral system came into existence. Different numeral systems were used across different countries and periods. The system adopted in India came to be known as the Indian numeral system or the Indian number system.
| 1. | What is the Indian Number System? |
| 2. | Number Names in the Indian Number System |
| 3. | Difference between Indian and International Number System |
| 4. | FAQs on the Indian Numeral System |
What is the Indian Number System?
The Indian numeral system contains numerals that are used to represent numbers. This system can be distinguished from the other numeral systems based on the nomenclature followed for different place values. When we use the Indian numeral system, we count with ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, and crores.
The following table depicts the different periods and the place values according to the number of digits in a number.
Use of Separators
According to the Indian numeral system, separators (comma) are used after every period while representing a number in its standard numeral form. For example, the number 384756182 can be better represented as 38,47,56,182 in the standard Indian numeral system using separators after every period. It should be noted that in the Indian numeral system, the periods are divided according to the rule of 3:2:2. This means that starting from the right, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. For example, notice the commas in the following number: 6,95,42,189.
Number Names in the Indian Number System
The number names in the Indian numeral system depend upon the nomenclature for different place values of digits in the number. While writing number names of the numerals in the Indian system, we should consider the following points:
- According to the Indian numeral system, separators (commas) are marked to distinguish different periods. Therefore, while writing the number names, these periods can be used to read the different place values in the number.
- In the Indian numeral system, the periods are divided according to the rule of 3:2:2 as discussed above and then the number name can be easily written.
- The periods in the Indian number system are expressed as, ones, thousands, lakhs and crores.
- So, we start writing the name of the period after each number in the period and we skip the period which has zeros at all places.
Let us take an example of writing a number name according to the Indian number system.
Example: Using the rules of the Indian number system, place the commas correctly in the given number and write the number name for 384756182.
Solution:
The following figure shows how to write the number name for 38,47,56,182, with the help of the Indian place value chart. We read the number according to the place values of all the digits given here.
According to the Indian numeral system, 384756182 is written as 38,47,56,182 after placing the commas. Then, its number name is written as thirty-eight crore, forty-seven lakh, fifty-six thousand, one hundred eighty-two.
Difference between Indian and International Number System
The main difference between the Indian and International numeration systems is the placement of the separators (commas) and the nomenclature of different place values. The International numeral system is used worldwide. When we count in terms of ones, hundreds, thousands, ten thousand, hundred thousand, millions, and billions, we are referring to the International numeral system. The following table depicts different places and periods according to the number of digits in a number.
The following table highlights the differences between the Indian and the International numeral system.
| Indian Numeral System | International Numeral System |
|---|---|
| Nine places are grouped into four periods: ones, thousands, lakhs, and crores. | Nine places are grouped into three periods: ones, thousands, and millions. |
| Place Values: ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores. | Place Values: Ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million. |
| Lakhs and crores are used in the Indian Numeral System. | Millions and billions are used in the International Numeral System. |
Let us place the commas and write the number name of a large number according to the Indian number system and as per the International number system.
Example: Rewrite the number 1347823 in the International numeral system and the Indian numeral system, using commas. Write the number name of the given number as per the Indian numeral system and as per the International numeral system.
Solution:
In the International numeral system, we begin from the right side and insert commas after every three digits. We divide the number into periods and read the period separately.
Standard International numeral system: 1,347,823
Number Name: One million, three hundred forty-seven thousand, eight hundred twenty-three.
The same given number, 1347823, can be written in the Indian numeral system, in the following way:
Standard Indian numeral system: 13,47,823
Number Name: Thirteen lakh, Forty-seven thousand, eight hundred twenty-three.
☛ Related Topics
FAQs on Indian Numeral System
What is the Indian Number System in Math?
The Indian numeral system is a writing system adapted in India for expressing numbers. It is a mathematical notation for representing numbers of a given set, using digits in a consistent manner. In the Indian number system, the place values of digits are read in the order of Ones, Tens, Hundreds, and so on, based on the nomenclature of the different periods.
What is the Difference Between the Indian and the International Numeral System?
The differences between the Indian and the International numeral system are given as follows:
- In the Indian numeral system, nine places are grouped into three periods: ones, thousands, lakhs, and crores. While, in the International number system nine places are grouped into the following periods: ones, thousands, and millions.
- In the Indian numeral system, the place values are marked as ones, tens, hundreds, thousands, ten thousand, lakhs, ten lakhs, crores, and ten crores. While, in the International numeral system, place values are marked as ones, tens, hundreds, thousands, ten thousand, hundred thousand, millions, ten million, and hundred million, and so on.
- The use of separators (commas) is different for both the Indian and International numeral systems, depending upon the periods. For example, in the Indian number system, the periods are divided according to the rule of 3:2:2. This means starting from the right, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. Whereas, in the International number system, the periods are divided according to the rule of 3: 3: 3. This means starting from the right, the first comma is placed after 3 digits, then the next commas are also placed after every 3 digits.
How are Numerals Written in the Indian System?
The numbers in the Indian numeral system are separated by commas (separators) after every period, as defined by this system. Starting from the right end, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. For example, the number 781700182 is written as 78,17,00,182.
How to Write Number Names in the Indian Numeral System?
When numbers are expressed in the form of words, the representation is termed as its number name. In the Indian numeral system, the number names depend on the different place values of digits in the number. While writing number names, we should know the place value of each digit according to the Indian place value system. The separators (commas) help us to read the place values of the numbers as we start writing them from left to right. So, we start writing the name of the period after each number in the period and we skip the period which has zeros at all places. For example, the number name for 41,27,56,082 is written as forty-one crore, twenty-seven lakh, fifty-six thousand, eighty-two.
What Comes after 10 crores in the Indian System?
The place value that comes after 10 crores is 100 crores or 1 Arab.
How to put Commas in the Indian Numeral System?
In the Indian numeral system, the periods are divided according to the rule of 3:2:2. This means starting from the right, the first comma is placed after 3 digits, then the next commas are placed after every 2 digits. For example, let us observe the commas in the following number: 8,24,76,217. The number name for this number is written as, eight crores, twenty-four lakh, seventy-six thousand, two hundred seventeen.